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Step Ahead Numbers
the Mathematics Enrichment Program
offered in connection with MATH 010,
Queen's University, Fall 2007
Thank you for the opportunity to provide the enrichment program. We hope your
students enjoyed it as much as we did. The topics we covered with your students,
including the activities used, are checked off below:
TOPICS COVERED
1. Number Patterns and Explanations
□ Examples of patterns in number
sequences
□ An exploration of infinite sets
□ An introduction/review of the use
of formulas in mathematics
□ The distinction between the pattern
rule and the resulting sequence
2. Growth Rates of Sequences
□ Why different sequences grow at
very different rates
□ Measuring growth rates (using a
story about magic boxes)
□ Exponential notation for powers
higher than squares
3. Division
□ Divisibility tricks (by 2, 3, 4, 5 & 9)
□ Prime number factorization
□ Estimating the digits in 213466917-1,
the largest known prime number
□ Applications to greatest common
factor and least common multiple
4. Fractions
□ Fractions that correspond to both
terminating and repeating decimals
□ Rational and irrational numbers
□ √2 as an irrational number
□ Decimal expressions and the
number line
ENRICHMENT ACTIVITIES
□ E.A. 1.1 – Recognizing Patterns
□ E.A. 1.2 – The Infinite Motel
□ E.A. 1.3 – Pattern Rules Producing
the Same Sequence
□ E.A. 1.4 – The Role of Proof
□ E.A. 1.5 – Patterns Produced
Geometrically
□ E.A. 2.1 – Measuring the Growth
Rate of a Sequence
□ E.A. 2.2 – The Poor Soldier and the
King
□ E.A. 3.1 – Prime Number Factors
□ E.A. 3.2 – What Prime Factors Tell
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You
E.A. 3.3 – Number Magic
E.A. 3.4 – How Many Primes Are
There?
E.A. 3.5 – Greatest Common Factor
E.A. 3.6 – Least Common Multiple
P.S. 3.7 – Practice Using Prime
Factorizations
E.A. 4.1 – Fractions and Decimals
E.A. 4.2 – Terminating or Repeating?
P.S. 4.3 – Practice with Fractions and
Decimals
E.A. 4.4 – Rational and Irrational
Numbers
E.A. 4.5 – The Difference Between
0.99999… and 1
continued on back
5. Remainders
□ Simple modular arithmetic
(arithmetic that focuses on the
remainders left after division by a
prime number)
□ An explanation of the trick for
divisibility by 3, using modular
arithmetic
6. Counting
□ Counting and organizing large
collections
□ Interpreting a counting problem and
finding the appropriate mathematics
to model it
7. Probability
□ Introduction to probability as a
problem of counting a set of equally
likely outcomes
□ Calculating probabilities
□ The concept of risk (a concept
combining probability and cost) and
risk calculations
Other
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□ E.A. 5.1 – Some Strange Division
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Problems
E.A. 5.2 – Jelly Beans
E.A. 5.3 - Multiplication
P.S. 5.4 – Apples and Oranges
E.A. 5.5 - Leftovers
□ E.A. 6.1 – Finding a System
□ P.S. 6.2 – Counting Practice
□ E.A. 6.3 – Coins and Dice
□ E.A. 7.1 – Equally Likely
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Outcomes
P.S. 7.2 – Probability Practice
E.A. 7.3 – Should we be Surprised?
P.S. 7.4 – More Practice
E.A. 7.5 – What is the Risk?